In this paper we present an autonomous robotic system for picking, transporting, and precisely placing magnetically graspable objects. Such a system would be especially beneficial for construction tasks where human presence is not possible, e.g. due to chemical or radioactive pollution. The system comprises of two primary components – a wheeled, mobile platform and a manipulator arm. Both are interconnected through an onboard computer and utilize various onboard sensors for estimating the state of the robot and its surroundings. By using efficient processing algorithms, data from the onboard sensors can be used in a feedback loop during all critical operational sections, resulting in a robust system capable of operating on uneven terrain and in environments without access to satellite navigation. System functionality has been proven in Challenge II of the MBZIRC 2020 competition. The Challenge required a ground robot to build an L-shaped structure of colored bricks laid in a predefined pattern. Such a mission incorporates several demanding subchallenges, spanning multiple branches of computer science, cybernetics, and robotics. Moreover, all the subchallenges had to be performed flawlessly in rapid succession, in order to complete the Challenge successfully. The extreme difficulty of the task was highlighted in the MBZIRC 2020 finals, where our system was among the only two competitors (out of 32) that managed to complete the task in autonomous mode.